Representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909470454448128 |
|---|---|
| author | Takahashi, Nobuyoshi |
| author_facet | Takahashi, Nobuyoshi |
| contents | Let $T$ be a Lie-Yamaguti algebra such that its standard enveloping Lie algebra $L(T)$ is semisimple and $[T, T, T]=T$. Then we give a description of representations of $T$ in terms of representations of $L(T)$ with certain additional data. Similarly, if $(T, σ)$ is an infinitesimal $s$-manifold such that $L(T)$ is semisimple, then any representation of $(T, σ)$ comes from a representation of $L(T)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras Takahashi, Nobuyoshi Rings and Algebras Representation Theory Primary 17A30, Secondary 17A40, 17B60, 22F30 Let $T$ be a Lie-Yamaguti algebra such that its standard enveloping Lie algebra $L(T)$ is semisimple and $[T, T, T]=T$. Then we give a description of representations of $T$ in terms of representations of $L(T)$ with certain additional data. Similarly, if $(T, σ)$ is an infinitesimal $s$-manifold such that $L(T)$ is semisimple, then any representation of $(T, σ)$ comes from a representation of $L(T)$. |
| title | Representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras |
| topic | Rings and Algebras Representation Theory Primary 17A30, Secondary 17A40, 17B60, 22F30 |
| url | https://arxiv.org/abs/2407.16932 |